This is the first article in a series of three dealing with the exploitation of speckle for imaging purposes. Speckle is the complex interference wave-field produced by a random distribution of unresolved scatterers. In this paper, we show how these scatterers can be used as virtual microphones to monitor the spatio-temporal propagation of a wave-packet inside the medium. To do so, the concept of matrix imaging is particularly useful. It consists in decoupling the location of the transmitted and received focal spots in a standard beamforming process. By scanning the wave-field with the output focal spot that then acts as a virtual transducer, one can image the spatio-temporal evolution of the wave-packet inside the medium. This unique observable will allow us to highlight the imperfections of the focusing process, in particular the defocus and reverberations induced by a strong aberrating layer. As a proof-of-concept, we will consider ultrasound experiments on tissue-mimicking phantoms. In the next two papers, we will show how this observable can be leveraged to compensate for these phenomena that hamper wave focusing and imaging in all fields of wave physics. Our method is indeed broadly applicable to different types of waves beyond ultrasound for which multi-element technology allows a reflection matrix to be measured.